On the minimal area of quadrangles circumscribed about planar convex bodies

TL;DR

This paper proves that every planar convex body can be enclosed in a quadrangle with an area very close to the minimal possible, improving previous bounds.

Contribution

It establishes a tighter upper bound on the minimal area of quadrangles circumscribed about planar convex bodies.

Findings

New upper bound for quadrangle area relative to convex body

Improvement over previous best known bounds

Quantitative measure of minimal enclosing quadrangles

Abstract

We show that every planar convex body is contained in a quadrangle whose area is less than $(1 - 2.6 \cdot 10^{-7}) \sqrt{2}$ times the area of the original convex body, improving the best known upper bound by W. Kuperberg.